A Story of 5DWLRV®
Eureka Math™
Grade , Module Student)LOH_B
Contains Sprint and Fluency, Exit Ticket,
and Assessment Materials
Published by the non-profit Great Minds.
Copyright © 2015 Great Minds. All rights reserved. No part of this work may be reproduced or used in any
form or by any means — graphic, electronic, or mechanical, including photocopying or information storage and
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registered trademarks of Great Minds.
Printed in the U.S.A.
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10 9 8 7 6 5 4 3 2 1
Sprint and Fluency Packet
Lesson 2
A STORY OF RATIOS
7ͻϯ
Number Correct: ______
Generating Equivalent Expressions—Round 1
Directions: Write each as an equivalent expression in standard form as quickly and as accurately as possible within the
allotted time.
23. 4‫ ݔ‬+ 6‫ ݔ‬െ 12‫ݔ‬
1.
1+1
2.
1+1+1
3.
(1 + 1) + 1
4.
(1 + 1) + (1 + 1)
25. 7‫ ݔ‬െ 2‫ ݔ‬+ 3
5.
(1 + 1) + (1 + 1 + 1)
27. (4‫ ݔ‬+ 3) + 2‫ݔ‬
6.
‫ݔ‬+‫ݔ‬
28. (4‫ ݔ‬+ 3) + 3‫ݔ‬
(‫ ݔ‬+ ‫ )ݔ‬+ ‫ݔ‬
30. (4‫ ݔ‬+ 3) + 6‫ݔ‬
7.
8.
9.
24. 4‫ ݔ‬െ 6‫ ݔ‬+ 4‫ݔ‬
26. (4‫ ݔ‬+ 3) + ‫ݔ‬
‫ݔ‬+‫ݔ‬+‫ݔ‬
29. (4‫ ݔ‬+ 3) + 5‫ݔ‬
(‫ ݔ‬+ ‫ )ݔ‬+ (‫ ݔ‬+ ‫)ݔ‬
31. (11‫ ݔ‬+ 2) െ 2
10. (‫ ݔ‬+ ‫ )ݔ‬+ (‫ ݔ‬+ ‫ ݔ‬+ ‫)ݔ‬
11. (‫ ݔ‬+ ‫ ݔ‬+ ‫ )ݔ‬+ (‫ ݔ‬+ ‫ ݔ‬+ ‫)ݔ‬
12. 2‫ ݔ‬+ ‫ݔ‬
13. 3‫ ݔ‬+ ‫ݔ‬
32. (11‫ ݔ‬+ 2) െ 3
33. (11‫ ݔ‬+ 2) െ 4
34. (11‫ ݔ‬+ 2) െ 7
35. (3‫ ݔ‬െ 9) + (3‫ ݔ‬+ 5)
14. 4‫ ݔ‬+ ‫ݔ‬
36. (11 െ 5‫ )ݔ‬+ (4‫ ݔ‬+ 2)
15. 7‫ ݔ‬+ ‫ݔ‬
37. (2‫ ݔ‬+ 3‫ )ݕ‬+ (4‫ ݔ‬+ ‫)ݕ‬
38. (5‫ ݔ‬+ 1.3‫ )ݕ‬+ (2.9‫ ݔ‬െ 0.6‫)ݕ‬
16. 7‫ ݔ‬+ 2‫ݔ‬
39. (2.6‫ ݔ‬െ 4.8‫ )ݕ‬+ (6.5‫ ݔ‬െ 1.1‫)ݕ‬
17. 7‫ ݔ‬+ 3‫ݔ‬
3
1
7
5
40. ൬ ‫ ݔ‬െ ‫ݕ‬൰ + ൬െ ‫ ݔ‬െ ‫ݕ‬൰
4
2
4
2
2
7
7
2
41. ൬െ ‫ ݔ‬െ ‫ݕ‬൰ + ൬െ ‫ ݔ‬െ ‫ݕ‬൰
5
9
10
3
1
1
3
5
42. ൬ ‫ ݔ‬െ ‫ݕ‬൰ + ൬െ ‫ ݔ‬+ ‫ݕ‬൰
2
4
5
6
3
3
43. ൬1.2‫ ݔ‬െ ‫ݕ‬൰ െ ൬െ ‫ ݔ‬+ 2.25‫ݕ‬൰
4
5
5
2
44. (3.375‫ ݔ‬െ 8.9‫ )ݕ‬െ ൬െ7 ‫ ݔ‬െ 5 ‫ݕ‬൰
8
5
18. 10‫ ݔ‬െ ‫ݔ‬
19. 10‫ ݔ‬െ 5‫ݔ‬
20. 10‫ ݔ‬െ 10‫ݔ‬
21. 10‫ ݔ‬െ 11‫ݔ‬
22. 10‫ ݔ‬െ 12‫ݔ‬
Lesson 2:
Generating Equivalent Expressions
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Lesson 2
A STORY OF RATIOS
7ͻϯ
Number Correct: ______
Improvement: ______
Generating Equivalent Expressions—Round 2
Directions: Write each as an equivalent expression in standard form as quickly and as accurately as possible within the
allotted time.
23. 3‫ ݔ‬+ 5‫ ݔ‬െ 4‫ݔ‬
1.
1+1+1
2.
1+1+1+1
3.
(1 + 1 + 1) + 1
4.
(1 + 1 + 1) + (1 + 1)
5.
(1 + 1 + 1) + (1 + 1 + 1)
26. (9‫ ݔ‬െ 1) + ‫ݔ‬
6.
‫ݔ‬+‫ݔ‬+‫ݔ‬
28. (9‫ ݔ‬െ 1) + 3‫ݔ‬
7.
8.
9.
24. 8‫ ݔ‬െ 6‫ ݔ‬+ 4‫ݔ‬
‫ݔ‬+‫ݔ‬+‫ݔ‬+‫ݔ‬
25. 7‫ ݔ‬െ 4‫ ݔ‬+ 5
27. (9‫ ݔ‬െ 1) + 2‫ݔ‬
29. (9‫ ݔ‬െ 1) + 5‫ݔ‬
(‫ ݔ‬+ ‫ ݔ‬+ ‫ )ݔ‬+ ‫ݔ‬
(‫ ݔ‬+ ‫ ݔ‬+ ‫ )ݔ‬+ (‫ ݔ‬+ ‫)ݔ‬
10. (‫ ݔ‬+ ‫ ݔ‬+ ‫ )ݔ‬+ (‫ ݔ‬+ ‫ ݔ‬+ ‫)ݔ‬
11. (‫ ݔ‬+ ‫ ݔ‬+ ‫ ݔ‬+ ‫ )ݔ‬+ (‫ ݔ‬+ ‫)ݔ‬
12. ‫ ݔ‬+ 2‫ݔ‬
13. ‫ ݔ‬+ 4‫ݔ‬
30. (9‫ ݔ‬െ 1) + 6‫ݔ‬
31. (െ3‫ ݔ‬+ 3) െ 2
32. (െ3‫ ݔ‬+ 3) െ 3
33. (െ3‫ ݔ‬+ 3) െ 4
34. (െ3‫ ݔ‬+ 3) െ 5
35. (5‫ ݔ‬െ 2) + (2‫ ݔ‬+ 5)
14. ‫ ݔ‬+ 6‫ݔ‬
36. (8 െ ‫ )ݔ‬+ (3‫ ݔ‬+ 2)
15. ‫ ݔ‬+ 8‫ݔ‬
37. (5‫ ݔ‬+ ‫ )ݕ‬+ (‫ ݔ‬+ ‫)ݕ‬
5
3
11
3
38. ൬ ‫ ݔ‬+ ‫ݕ‬൰ + ൬ ‫ ݔ‬െ ‫ݕ‬൰
2
2
2
4
1
3
2
7
39. ൬ ‫ ݔ‬െ ‫ݕ‬൰ + ൬ ‫ ݔ‬െ ‫ݕ‬൰
6
8
3
4
16. 7‫ ݔ‬+ ‫ݔ‬
17. 8‫ ݔ‬+ 2‫ݔ‬
40. (9.7‫ ݔ‬െ 3.8‫ )ݕ‬+ (െ2.8‫ ݔ‬+ 4.5‫)ݕ‬
18. 2‫ ݔ‬െ ‫ݔ‬
19. 2‫ ݔ‬െ 2‫ݔ‬
41. (1.65‫ ݔ‬െ 2.73‫ )ݕ‬+ (െ1.35‫ ݔ‬+ 3.76‫)ݕ‬
20. 2‫ ݔ‬െ 3‫ݔ‬
42. (6.51‫ ݔ‬െ 4.39‫ )ݕ‬+ (െ7.46‫ ݔ‬+ 8.11‫)ݕ‬
2
7
1
43. ൬0.7‫ ݔ‬െ ‫ݕ‬൰ െ ൬െ ‫ ݔ‬+ 2 ‫ݕ‬൰
9
5
3
1
3
44. (8.4‫ ݔ‬െ 2.25‫ )ݕ‬െ ൬െ2 ‫ ݔ‬െ 4 ‫ݕ‬൰
2
8
21. 2‫ ݔ‬െ 4‫ݔ‬
22. 2‫ ݔ‬െ 8‫ݔ‬
Lesson 2:
Generating Equivalent Expressions
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Exit Ticket Packet
Lesson 1
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 1: Generating Equivalent Expressions
Exit Ticket
1.
Write an equivalent expression to 2‫ ݔ‬+ 3 + 5‫ ݔ‬+ 6 by combining like terms.
2.
Find the sum of (8ܽ + 2ܾ െ 4) and (3ܾ െ 5).
3.
Write the expression in standard form: 4(2ܽ) + 7(െ4ܾ) + (3 ή ܿ ή 5).
Lesson 1:
Generating Equivalent Expressions
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Lesson 2
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 2: Generating Equivalent Expressions
Exit Ticket
1.
Write the expression in standard form.
(4݂ െ 3 + 2݃) െ (െ4݃ + 2)
2.
Find the result when 5݉ + 2 is subtracted from 9݉.
3.
Write the expression in standard form.
ʹ͹݄ ÷ ͵݄
Lesson 2:
Generating Equivalent Expressions
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Lesson 3
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 3: Writing Products as Sums and Sums as Products
Exit Ticket
A square fountain area with side length ‫ ݏ‬ft. is bordered by two rows of square tiles along its perimeter as shown.
Express the total number of grey tiles (the second border of tiles) needed in terms of ‫ ݏ‬three different ways.
Lesson 3:
Writing Products as Sums and Sums as Products
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Lesson 4
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 4: Writing Products as Sums and Sums as Products
Exit Ticket
1.
Write the expression below in standard form.
3݄ െ 2(1 + 4݄)
2.
Write the expression below as a product of two factors.
6݉ + 8݊ + 4
Lesson 4:
Writing Products as Sums and Sums as Products
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Lesson 5
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 5: Using the Identity and Inverse to Write Equivalent
Expressions
Exit Ticket
1.
Find the sum of 5‫ ݔ‬+ 20 and the opposite of 20. Write an equivalent expression in standard form. Justify each
step.
2.
For 5‫ ݔ‬+ 20 and the multiplicative inverse of 5, write the product and then write the expression in standard form, if
possible. Justify each step.
Lesson 5:
Using the Identity and Inverse to Write Equivalent Expressions
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Lesson 6
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 6: Collecting Rational Number Like Terms
Exit Ticket
ଵ
For the problem ݃ െ
ହ
ଵ
ଵ଴
െ݃+1
ଷ
ଵ଴
݃െ
ଵ
ଵ଴
, Tyson created an equivalent expression using the following steps.
1
3
1
1
݃ + െ1݃ + 1 ݃ + െ
+െ
5
10
10
10
1
4
െ ݃+1
10
5
Is his final expression equivalent to the initial expression? Show how you know. If the two expressions are not
equivalent, find Tyson’s mistake and correct it.
Lesson 6:
Collecting Rational Number Like Terms
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Lesson 7
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 7: Understanding Equations
Exit Ticket
1.
Check whether the given value of ‫ ݔ‬is a solution to the equation. Justify your answer.
a.
b.
2.
ଵ
(‫ ݔ‬+ 4) = 20
‫ = ݔ‬48
3‫ ݔ‬െ 1 = 5‫ ݔ‬+ 10
‫ = ݔ‬െ5
ଷ
1
2
The total cost of four pens and seven mechanical pencils is $13.25. The cost of each pencil is 75 cents.
a.
Using an arithmetic approach, find the cost of a pen.
Lesson 7:
Understanding Equations
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Lesson 7
A STORY OF RATIOS
7ͻϯ
b.
Let the cost of a pen be ‫ ݌‬dollars. Write an expression for the total cost of four pens and seven mechanical
pencils in terms of ‫݌‬.
c.
Write an equation that could be used to find the cost of a pen.
d.
Determine a value for ‫ ݌‬for which the equation you wrote in part (b) is true.
e.
Determine a value for ‫ ݌‬for which the equation you wrote in part (b) is false.
Lesson 7:
Understanding Equations
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Lesson 8
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 8: Using If-Then Moves in Solving Equations
Exit Ticket
Mrs. Canale’s class is selling frozen pizzas to earn money for a field trip. For every pizza sold, the class makes $5.35.
They have already earned $182.90 toward their $750 goal. How many more pizzas must they sell to earn $750? Solve
this problem first by using an arithmetic approach, then by using an algebraic approach. Compare the calculations you
made using each approach.
Lesson 8:
Using If-Then Moves in Solving Equations
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Lesson 9
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 9: Using If-Then Moves in Solving Equations
Exit Ticket
1.
Brand A scooter has a top speed that goes 2 miles per hour faster than Brand B. If after 3 hours, Brand A scooter
traveled 24 miles at its top speed, at what rate did Brand B scooter travel at its top speed if it traveled the same
distance? Write an equation to determine the solution. Identify the if-then moves used in your solution.
2.
At each scooter’s top speed, Brand A scooter goes 2 miles per hour faster than Brand B. If after traveling at its top
speed for 3 hours, Brand A scooter traveled 40.2 miles, at what rate did Brand B scooter travel if it traveled the
same distance as Brand A? Write an equation to determine the solution and then write an equivalent equation
using only integers.
Lesson 9:
Using If-Then Moves in Solving Equations
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Lesson 10
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 10: Angle Problems and Solving Equations
Exit Ticket
In a complete sentence, describe the relevant angle relationships in the
following diagram. That is, describe the angle relationships you could use to
determine the value of ‫ݔ‬.
Use the angle relationships described above to write an equation to solve for ‫ݔ‬. Then, determine the measurements of
‫ ܪܣܬס‬and ‫ܩܣܪס‬.
Lesson 10:
Angle Problems and Solving Equations
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Lesson 11
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 11: Angle Problems and Solving Equations
Exit Ticket
Write an equation for the angle relationship shown in the figure and solve for ‫ݔ‬. Find the measures of ‫ ܴܵܳס‬and ‫ܷܳܶס‬.
Lesson 11:
Angle Problems and Solving Equations
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Lesson 12
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 12: Properties of Inequalities
Exit Ticket
1.
2.
Given the initial inequality െ4 < 7, state possible values for ܿ that would satisfy the following inequalities.
a.
ܿ(െ4) < ܿ(7)
b.
ܿ(െ4) > ܿ(7)
c.
ܿ(െ4) = ܿ(7)
Given the initial inequality 2 > െ4, identify which operation preserves the inequality symbol and which operation
reverses the inequality symbol. Write the new inequality after the operation is performed.
a.
Multiply both sides by െ2.
b.
Add െ2 to both sides.
c.
Divide both sides by 2.
d.
Multiply both sides by െ .
e.
Subtract െ3 from both sides.
1
2
Lesson 12:
Properties of Inequalities
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Lesson 13
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 13: Inequalities
Exit Ticket
Shaggy earned $7.55 per hour plus an additional $100 in tips waiting tables on Saturday. He earned at least $160 in all.
Write an inequality and find the minimum number of hours, to the nearest hour, that Shaggy worked on Saturday.
Lesson 13:
Inequalities
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Lesson 14
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 14: Solving Inequalities
Exit Ticket
Games at the carnival cost $3 each. The prizes awarded to winners cost $145.65. How many games must be played to
make at least $50?
Lesson 14:
Solving Inequalities
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Lesson 15
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 15: Graphing Solutions to Inequalities
Exit Ticket
The junior high art club sells candles for a fundraiser. The first week of the fundraiser, the club sells 7 cases of candles.
Each case contains 40 candles. The goal is to sell at least 13 cases. During the second week of the fundraiser, the club
meets its goal. Write, solve, and graph an inequality that can be used to find the possible number of candles sold the
second week.
Lesson 15:
Graphing Solutions to Inequalities
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Lesson 16
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 16: The Most Famous Ratio of All
Exit Ticket
Brianna’s parents built a swimming pool in the backyard. Brianna says that the distance around the pool is 120 feet.
1.
Is she correct? Explain why or why not.
2.
Explain how Brianna would determine the distance around the pool so that her parents would know how many feet
of stone to buy for the edging around the pool.
3.
Explain the relationship between the circumference of the semicircular part of the pool and the width of the pool.
Lesson 16:
The Most Famous Ratio of All
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Lesson 17
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 17: The Area of a Circle
Exit Ticket
Complete each statement using the words or algebraic expressions listed in the word bank below.
1.
The length of the
of
the rectangular region
approximates the length of
the
of the circle.
2.
The
of the rectangle
approximates the length of
one-half of the
circumference of the
circle.
3.
The circumference of the circle is _______________________.
4.
The _________________ of the ___________________ is 2‫ݎ‬.
5.
The ratio of the circumference to the diameter is ______.
6.
Area (circle) = Area of (_____________) =
1
1
ή circumference ή ‫( = ݎ‬2ߨ‫ )ݎ‬ή ‫ ߨ = ݎ‬ή ‫ ݎ‬ή ‫_____________ = ݎ‬.
2
2
Word bank
radius
height
base
૛࣊࢘
diameter
circle
rectangle
࣊࢘૛
Lesson 17:
The Area of a Circle
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࣊
18
Lesson 18
A STORY OF RATIOS
Name ___________________________________________________
7ͻϯ
Date____________________
Lesson 18: More Problems on Area and Circumference
Exit Ticket
1.
Ken’s landscape gardening business creates odd-shaped lawns that include semicircles. Find the area of this
semicircular section of the lawn in this design. Use
2.
22
for ߨ.
7
In the figure below, Ken’s company has placed sprinkler heads at the center of the two small semicircles. The radius
of the sprinklers is 5 ft. If the area in the larger semicircular area is the shape of the entire lawn, how much of the
lawn will not be watered? Give your answer in terms of ߨ and to the nearest tenth. Explain your thinking.
Lesson 18:
More Problems on Area and Circumference
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Lesson 19
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 19: Unknown Area Problems on the Coordinate Plane
Exit Ticket
The figure ‫ ܦܥܤܣ‬is a rectangle. ‫ = ܤܣ‬2 units, ‫ = ܦܣ‬4 units, and ‫ = ܥܨ = ܧܣ‬1 unit.
1.
Find the area of rectangle ‫ܦܥܤܣ‬.
2.
Find the area of triangle ‫ܧܤܣ‬.
4.
Find the area of the parallelogram ‫ ܨܦܧܤ‬two different ways.
Lesson 19:
3.
Find the area of triangle ‫ܨܥܦ‬.
Unknown Area Problems on the Coordinate Plane
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Lesson 20
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 20: Composite Area Problems
Exit Ticket
The unshaded regions are quarter circles. Approximate the area of the shaded region. Use ߨ ൎ 3.14.
Lesson 20:
Composite Area Problems
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21
Lesson 21
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 21: Surface Area
Exit Ticket
Find the surface area of the right trapezoidal prism. Show all necessary work.
Lesson 21:
Surface Area
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
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Lesson 22
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 22: Surface Area
Exit Ticket
1.
The right hexagonal pyramid has a hexagon base with equal-length sides. The
lateral faces of the pyramid are all triangles (that are exact copies of one
another) with heights of 15 ft. Find the surface area of the pyramid.
2.
Six cubes are glued together to form the solid shown in the
1
2
diagram. If the edges of each cube measure 1 inches in length,
what is the surface area of the solid?
Lesson 22:
Surface Area
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
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>ĞƐƐŽŶϮϯ
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 2ϯ: The Volume of a Right Prism
Exit Ticket
The base of the right prism is a hexagon composed of a rectangle and two triangles. Find the volume of the right
hexagonal prism using the formula ܸ = ‫݄ܤ‬.
>ĞƐƐŽŶϮϯ:
The Volume of a Right Prism
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
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Lesson 24
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 24: The Volume of a Right Prism
Exit Ticket
Lawrence poured 27.328 L of water into a right rectangular prism-shaped tank. The base of the tank is 40 cm by 28 cm.
2
3
When he finished pouring the water, the tank was full. (1 L = 1,000 cmଷ )
a.
How deep is the water in the tank?
b.
How deep is the tank?
c.
How many liters of water can the tank hold in total?
Lesson 24:
The Volume of a Right Prism
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
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Lesson 25
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 25: Volume and Surface Area
Exit Ticket
Melody is planning a raised bed for her vegetable garden.
15 in
30 in
48 in
a.
How many square feet of wood does she need to create the bed?
b.
She needs to add soil. Each bag contains 1.5 cubic feet. How many bags will she need to fill the vegetable
garden?
Lesson 25:
Volume and Surface Area
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
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Lesson 26
A STORY OF RATIOS
Name
7ͻϯ
Date
Lesson 26: Volume and Surface Area
Exit Ticket
Lawrence is designing a cooling tank that is a square prism. A pipe in the shape of a smaller 2 ft × 2 ft square prism
passes through the center of the tank as shown in the diagram, through which a coolant will flow.
a.
What is the volume of the tank including the cooling pipe?
b.
What is the volume of coolant that fits inside the cooling pipe?
c.
What is the volume of the shell (the tank not including the cooling pipe)?
d.
Find the surface area of the cooling pipe.
Lesson 26:
Volume and Surface Area
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
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